A gas turbine engine typically includes a compressor section, a combustor, and a turbine section. The compressor section compresses ambient air that enters an inlet. The combustor combines the compressed air with a fuel and ignites the mixture creating combustion products defining a working fluid. The working fluid travels to the turbine section where it is expanded to produce a work output. Within the turbine section are rows of stationary vanes directing the working fluid to rows of rotating blades coupled to a rotor. Each pair of a row of vanes and a row of blades form a stage in the turbine section.
Advanced gas turbines with high performance requirements attempt to reduce the aerodynamic losses as much as possible in the turbine section. This in turn results in improvement of the overall thermal efficiency and power output of the engine. One possible way to reduce aerodynamic losses is to incorporate endwall contouring on the blade and vane shrouds in the turbine section. Endwall contouring when optimized can result in a significant reduction in secondary flow vortices which may contribute to losses in the turbine stage.